Could an AI be built to learn based of interaction with a human?
In principle, yes, what you are proposing can be done.  The exact details of how to do it are an open research question.  The details would also depend on exactly what your goals for the system are. If you're just trying to build some domain specific system that learns a very specific kind of knowledge, then that's probably going to be easier than building an AGI that learns like a child does.  

What I will suggest, although this is not proven, is that building a really powerful system of this sort will probably require more than deep learning.  I would also caution anybody interested in AI against thinking that deep learning is the "be all, end all" of AI techniques. My guess is that doing this well will ultimately require a multi-agent system, maybe something like Minsky's "Society of Mind" approach, or a Blackboard model, with collaborating agents, each specialized for various aspects of intelligence.  My feeling is that you will, indeed, need deep learning for classification / pattern matching, but possibly also things like Case Based Reasoning, K-Lines, a Semantic Network, Rule Learning, BDI, and other techniques, working together.